Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON):

Solution:
def do_case(n):
    Ts = {}
    i = 1
    while True:
        t = i * (i + 1) / 2
        if t > 1E9:
            break
        if n - t > 0:
            Ts[t] = n - t
        i += 1

    tk = Ts.keys()
    for t in tk:
        try:
            if Ts[Ts[t]] == t:
                return "YES"
        except KeyError:
            pass

    return "NO"


def main():
    print do_case(int(raw_input()))

if __name__ == "__main__":
    main()